Expression of type ExprTuple

from the theory of proveit.linear_algebra.tensors

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprTuple, K, Lambda, i, j, k
from proveit.core_expr_types import A_1_to_i, B_1_to_j, C_1_to_k
from proveit.linear_algebra import TensorProd, VecSpaces
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([i, j, k], Conditional(Forall(instance_param_or_params = [A_1_to_i, B_1_to_j, C_1_to_k], instance_expr = Equals(TensorProd(A_1_to_i, B_1_to_j, C_1_to_k), TensorProd(A_1_to_i, TensorProd(B_1_to_j), C_1_to_k)).with_wrapping_at(1), domain = VecSpaces(K)).with_wrapping(), And(InSet(i, Natural), InSet(j, Natural), InSet(k, Natural)))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\left(i, j, k\right) \mapsto \left\{\begin{array}{l}\forall_{A_{1}, A_{2}, \ldots, A_{i}, B_{1}, B_{2}, \ldots, B_{j}, C_{1}, C_{2}, \ldots, C_{k} \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\\
\left(\begin{array}{c} \begin{array}{l} \left(A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{i}{\otimes} B_{1} {\otimes}  B_{2} {\otimes}  \ldots {\otimes}  B_{j}{\otimes} C_{1} {\otimes}  C_{2} {\otimes}  \ldots {\otimes}  C_{k}\right) \\  = \left(A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{i} {\otimes} \left(B_{1} {\otimes}  B_{2} {\otimes}  \ldots {\otimes}  B_{j}\right){\otimes} C_{1} {\otimes}  C_{2} {\otimes}  \ldots {\otimes}  C_{k}\right) \end{array} \end{array}\right)\end{array} \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N} ,  k \in \mathbb{N}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	42, 57, 46
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 23 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11, 12
9	Lambda	parameters: 30 body: 13
10	Operation	operator: 16 operands: 14
11	Operation	operator: 16 operands: 15
12	Operation	operator: 16 operands: 17
13	Conditional	value: 18 condition: 19
14	ExprTuple	42, 20
15	ExprTuple	57, 20
16	Literal
17	ExprTuple	46, 20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	Literal
21	Literal
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	27, 28, 29
25	Operation	operator: 43 operands: 30
26	Operation	operator: 43 operands: 31
27	ExprRange	lambda_map: 32 start_index: 56 end_index: 42
28	ExprRange	lambda_map: 33 start_index: 56 end_index: 57
29	ExprRange	lambda_map: 34 start_index: 56 end_index: 46
30	ExprTuple	35, 51, 37
31	ExprTuple	35, 36, 37
32	Lambda	parameter: 66 body: 38
33	Lambda	parameter: 66 body: 39
34	Lambda	parameter: 66 body: 40
35	ExprRange	lambda_map: 41 start_index: 56 end_index: 42
36	Operation	operator: 43 operands: 44
37	ExprRange	lambda_map: 45 start_index: 56 end_index: 46
38	Operation	operator: 49 operands: 47
39	Operation	operator: 49 operands: 48
40	Operation	operator: 49 operands: 50
41	Lambda	parameter: 66 body: 52
42	Variable
43	Literal
44	ExprTuple	51
45	Lambda	parameter: 66 body: 53
46	Variable
47	ExprTuple	52, 54
48	ExprTuple	62, 54
49	Literal
50	ExprTuple	53, 54
51	ExprRange	lambda_map: 55 start_index: 56 end_index: 57
52	IndexedVar	variable: 58 index: 66
53	IndexedVar	variable: 59 index: 66
54	Operation	operator: 60 operand: 63
55	Lambda	parameter: 66 body: 62
56	Literal
57	Variable
58	Variable
59	Variable
60	Literal
61	ExprTuple	63
62	IndexedVar	variable: 64 index: 66
63	Variable
64	Variable
65	ExprTuple	66
66	Variable